{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RGON4Q3EM2K3SQGEJVDBVTBG5Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8dd98690a885b978cdd827497efa95ba9e80202e80dbfb39490b4cd81730265b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-03-24T10:22:38Z","title_canon_sha256":"a4b873888d348161bf4adbbc49228826f702bd72bb13a93d7f61e31ee62f7f10"},"schema_version":"1.0","source":{"id":"1603.07509","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07509","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07509v1","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07509","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"RGON4Q3EM2K3","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RGON4Q3EM2K3SQGE","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RGON4Q3E","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:21849295ccef9aacd8c1b82a0b8aa734bf72d2c5d45965e709d29e64a5bc9bf9","target":"graph","created_at":"2026-05-18T01:18:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we show that every pseudo B-Fredholm operator is a pseudo Fredholm operator. Afterwards, we prove that the pseudo B-Weyl spectrum is empty if and only if the pseudo B-Fredholm spectrum is empty. Also, we study a symmetric difference between some parts of the spectrum.","authors_text":"Abdelaziz Tajmouati, Mohamed Amouch, Mohamed Karmouni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-03-24T10:22:38Z","title":"Pseudo B-Fredholm Operators and Spectral Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07509","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f11d7ab3437b69940a2e1e9fcaca84a4d57286e0fbaa67a3f27591acdf1d362d","target":"record","created_at":"2026-05-18T01:18:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8dd98690a885b978cdd827497efa95ba9e80202e80dbfb39490b4cd81730265b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-03-24T10:22:38Z","title_canon_sha256":"a4b873888d348161bf4adbbc49228826f702bd72bb13a93d7f61e31ee62f7f10"},"schema_version":"1.0","source":{"id":"1603.07509","kind":"arxiv","version":1}},"canonical_sha256":"899cde43646695b940c44d461acc26ec28b706eca9c83584ca3db41643da4d27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"899cde43646695b940c44d461acc26ec28b706eca9c83584ca3db41643da4d27","first_computed_at":"2026-05-18T01:18:20.682481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:20.682481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sf3DpjVLUGlv0h391e6q5fwwLwwtSdVOlZzOs/vRA6/++1GWdTyp6yy8bsromyYYrunC0hSVhqE5zlQZZGBvDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:20.683003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07509","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f11d7ab3437b69940a2e1e9fcaca84a4d57286e0fbaa67a3f27591acdf1d362d","sha256:21849295ccef9aacd8c1b82a0b8aa734bf72d2c5d45965e709d29e64a5bc9bf9"],"state_sha256":"3b6083d4f7d375cdf07823d4d8c6a0da5e15b805b1c02be6e1700cfed0769b13"}